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Polynomial level-set methods for nonlinear dynamical systems analysis
dynamical systems analysis level-set methods
2015/6/19
In this paper, we present a method for computing the domain of attraction for non-linear dynamical systems. We propose a level-set method where sets are represented as sublevel sets of polynomials. Th...
Solitary and periodic wave solutions in quadratic nonlinear media
solitary waves periodic waves the theory of dynamical systems
2011/10/20
By using the theory of dynamical systems, solitary and periodic wave solutions for a coupled quadratic nonlinear system are studied.
Nonlinear Analysis of the Solutions of the Hasegawa-Wakatani Equations
Hasegawa Wakatani equations centre manifold theory nonlinear ordinary differential equations
2011/8/22
Abstract: The Hasegawa-Wakatani models are used in the study of confinement of hot plasmas with externally imposed magnetic fields. The nonlinear terms in the Hasegawa-Wakatani models complicate the a...
Nonlinear dynamics of two coupled nano-electromechanical resonators
Nonlinear dynamics coupled nano-electromechanical resonators
2011/7/6
As a model of coupled nano-electromechanical resonantors we study two nonlinear driven oscillators with an arbitrary coupling strength between them. Analytical expressions are derived for the oscillat...
Instabilities in free surface continuous jets of non-Newtonian fluids, although relevant for many industrial processes, remain less well understood in terms of fundamental fluid dynamics.
Nonlinear dynamics of a coupled micro-ring resonator chain
Nonlinear dynamics coupled micro-ring resonator chain
2010/12/28
We study nonlinear wave phenomena in a coupled ring resonator optical waveguide in the tight coupling regime. The discrete nonlinear Bloch modes of the structure are derived. The switching behavior of...
Forced Nonlinear Resonance in a System of Coupled Oscillators
Forced Nonlinear Resonance System of Coupled Oscillators
2010/12/28
We consider a resonantly perturbed system of coupled nonlinear oscillators with small dissipation and outer periodic perturbation. We show that for the large time t ∼ "−2 one component of ...
Dynamics of ring dark solitons in Bose-Einstein condensates and nonlinear optics
Pattern Formation and Solitons (nlin.PS) Quantum Gases (cond-mat.quant-gas)
2010/11/10
Quasiparticle approach to dynamics of dark solitons is applied to the case of ring solitons. It is shown that the energy conservation law provides the effective equations of motion of ring dark solito...
Global dynamics above the ground state for the nonlinear Klein-Gordon equation without a radial assumption
Global dynamics above the ground state the nonlinear Klein-Gordon equation
2010/11/8
We extend our previous result on the focusing cubic Klein-Gordon equation in three dimensions to the non-radial case, giving a complete classification of global dynamics of all solutions with energy a...
Nearly linear dynamics of nonlinear dispersive waves
Nearly linear dynamics nonlinear dispersive waves
2010/12/14
Dispersive averaging e ects are used to show that KdV equation with periodic boundary conditions possesses high frequency solutions which behave nearly linearly.
Modeling scaled processes and 1/f^b noise by the nonlinear stochastic differential equations
nonlinear stochastic differential power-law distributions
2010/4/2
We present and analyze stochastic nonlinear differential equations generating signals with the power-law distributions of the signal intensity, 1/f^b noise, power-law autocorrelations and second order...
Regularity of coupled two-dimensional Nonlinear Fokker-Planck and Navier-Stokes Systems
Nonlinear Fokker-Planck equations Navier-Stokes equations microscopic variables Deborah number
2014/4/4
We consider systems of particles coupled with fluids. The particles are described by the evolution of their density, and the fluid is described by the Navier-Stokes equations. The particles add stress...
Nonlinear Fokker-Planck Navier-Stokes Systems
Fokker-Planck equations Navier-Stokes equations Smoluchowski equations microscopic inclusions
2014/4/4
We consider Navier-Stokes equations coupled to nonlinear FokkerPlanck equations describing the probability distribution of particles interacting with fluids. We describe relations determining the coef...